Some types of electric loads are subject to rapid variations of the absorbed current. The variation may go from an almost null current to the nominal maximum current and vice versa. The regulator (generally a switching regulator) that supplies these loads must be capable of maintaining the regulated voltage in a pre-defined range of accuracy (dynamic precision), which is often very narrow. For instance, processors used in portable computers supplied by batteries mostly in a stand-by mode during which their consumption is relatively low and from which they resume operation when instructions must be carried out.
The commonly used regulators have a closed loop control of the output voltage VOUT to ensure under steady state conditions, i.e. with a constant load, that the regulated voltage is equal to the desired voltage VREF independently from the load and the input voltage of the regulator. Of course, during a load transient this is no longer true. The speed with which the regulator adjusts the output voltage to the desired voltage VREF, depends on the type of control used by the regulator and on the characteristics of the power stage.
Regulators that implement a control with hysteresis of the output voltage, as the regulator depicted in FIG. 1, generally provide for the fastest response to a load transient and are the most commonly used. Because of the importance of these regulators, in the ensuing description reference will be made to regulators with hysteresis, but the discussion also applies to regulators without hysteresis. Moreover, it will be discussed in detail the operation of known regulators with a high side power switch (HS) that switches the inductor to the supply voltage source. However, this is influential in identifying the particular technical problem being addressed and which is present also in regulators of different topology (for instance step-up regulators) wherein the inductor is switched to ground by a low side (LS) switch instead of to the supply voltage source.
A comparator with hysteresis of the output voltage VOUT and the reference voltage VREF determines the turn on and the turn off of the switch HS of the branch toward the node at the highest potential of an output half-bridge. If a constant turn on time (TON) control is carried out, a comparator without hysteresis is used instead and the switch HS remains on for a fixed time TON once it is turned on, while in a constant turn off time (TOFF) control mode, the comparator switches off the switch HS. The kinds of controls mentioned above contemplate also variants in which the equivalent voltage at the input of the comparator is the integral-proportional voltage error (V2 control) or the sum of the integral-proportional error and of a voltage proportional to the current in the inductor (current-mode control).
In a so-called forced turn on control (or forced turn off), a clock signal is provided to the command logic CONTROL LOGIC that forces the turn on (the turn off) of the switch HS with a period TS, while the turn off (turn on) instant is determined by the comparator. Sometimes a minimum turn on time TON,MIN (minimum turn off time TOFF,MIN) of the switch HS is imposed. Typically, in these kinds of synchronous control a current mode control is implemented. A saw-tooth signal synchronous with the clock is usually applied to an input of the comparator for preventing sub-harmonic instability.
In a PWM control, a modulator varies the duty-cycle proportionally to a control (voltage) signal applied to an input thereof. The turn on of the switch HS is usually synchronous with an external clock. The voltage integral-proportional error is applied at the control input. These regulators are relatively slow at regulating the output voltage to its reference value after a load variation has occurred, because they are never capable of reacting sufficiently fast to a very fast load transient.
For these reasons, an output capacitor in parallel to the load is capable, within certain limits, of allowing for an abrupt increase of the current absorption of the load while limiting the error on the output voltage. In general, the output capacitor has a non-negligible parasitic series resistance ERS dependent on the capacitance of the output capacitor COUT. The corresponding time constant TC=ESR·COUT depends on the type of capacitor (tantalum, ceramic, organic electrolytic, etc.) and is to a large extent independent of the capacitance.
The power switch (or switches) has also an influence, besides the controller, in determining the effective response speed of the regulator. There is in fact a limit to the speed (slew-rate limitation) of variation of the current that the output power stage may furnish to the electric parallel of the load and of the output capacitor. For instance, if the switch HS is turned on, the current iL circulating in the inductor cannot increase at a speed greater than                                                         ⅆ                              i                L                                                    ⅆ              t                                ≤                      m            p                          =                                            V              IN                        -                          V              OUT                                L                                    (        1        )                            while, if the switch HS is turned off, the current cannot fall at a speed smaller than                                                         ⅆ                              i                L                                                    ⅆ              t                                ≥                      -                          m              m                                      =                  -                                                    V                OUT                            L                        .                                              (        2        )                    
In a regulator with constant turn on time, phases of duration TON during which the switch HS is turned on alternate with phases of duration TOFF,MIN during which the switch is turned off, thus the mean speed variation of the output current is                               m          p                =                              (                                                            T                  ON                                ·                                                                            V                      IN                                        -                                          V                      OUT                                                        L                                            -                                                T                                      OFF                    ,                    MIN                                                  ·                                                      V                    OUT                                    L                                                      )                    ·                                    1                                                T                  ON                                +                                  T                                      OFF                    ,                    MIN                                                                        .                                              (        3        )            
If for example the output current undergoes to a step increase ΔIOUT, the output voltage VOUT drops abruptly by an amount equal to ESR·ΔIOUT. Depending on the response speed of the regulator, the output voltage VOUT may thereafter raise back to the reference voltage or continue falling. For instance, in a regulator with hysteresis (e.g. with a constant turn on time TON), if the voltage VOUT is lower than the reference voltage, the output current IOUT increases with a slope given by eq. 1 (eq. 3). The output voltage will not fall further if                               m          p                ≥                                            Δ              ⁢                                                           ⁢                              I                OUT                                                    ESR              ·                              C                OUT                                              .                                    (        4        )            
FIG. 2 depicts the waveforms of the main signals of the regulator with hysteresis of FIG. 1 after a load increase, being:                ΔIOUT=20A; L=1.2 μH; VIN=12V; VREF0.5V; ESR=4 mΩ;        hysteresis=20 mV; COUT=2 mF.        
Eq. 4 is verified, thus the output voltage cannot fall more than ESR·ΔIOUT. FIG. 3 is the response of the regulator of FIG. 1 after a load reduction of the same absolute value. By substituting mm to mp, eq. 4 is no longer satisfied, thus the overshoot exceeds ESR·ΔIOUT. Indicating with ΔVOUT,MAX the maximum variation of the output voltage and with ΔIOUT,MAX the maximum variation of the output current, to satisfy the dynamic specifications the capacitance of the output capacitor must be such to ensure that                                           ESR            ·            Δ                    ⁢                                           ⁢                      I                          OUT              ,              MAX                                      ≤                              1            2                    ⁢          Δ          ⁢                                           ⁢                      V                          OUT              ,              MAX                                                          (        5        )                            wherein the voltage VOUT must range between VREF±ΔVOUT,MAX/2.        
The area occupied by the output capacitor COUT and the costs thereof (which are proportional to the capacitance, and inversely proportional to the parasitic resistance ESR) have a great importance in this kind of application. The so-called “voltage positioning” technique, often used for reducing the capacitance of the output capacitor, consists in modifying the controller so that the output resistance of the regulator under steady state conditions RO is not null, and in choosing the reference voltage V′REF:                               V          REF          ′                =                              V            REF                    +                                                    Δ                ⁢                                                                   ⁢                                  V                                      OUT                    ,                    MAX                                                              2                        .                                              (        6        )            
In this way, the null load voltage is higher than the desired voltage VREF while at maximum load, under steady state conditions, is lower.
IfRO=ESR  (7)                 then the static variation, i.e. the voltage variation after the load transient has terminated, is equal to the dynamic variation, i.e. the variation that immediately follows the load transient.        
Finally, if an appropriate controller for making the regulator operate as a pure resistance of value ESR even under transient conditions is realized, that is for making the output impedance ZOUT=ESR, then the variation of the output voltage after a step variation ΔIOUT of the output current is a voltage step variation ESR·ΔIOUT. An example of response of a regulator with ZOUT=ESR is depicted in FIG. 6. The specifications of dynamic accuracy are now satisfied ifESR·ΔIOUT,MAX≦ΔVOUT,MAX  (8) 
Therefore, it is possible to use a capacitor whose capacitance is half the value of the previous evaluation.
The condition ZOUT=ESR ensures that the output voltage VOUT remains in the dynamic accuracy range even if two load transients, from zero to the maximum load and vice versa, occur in rapid succession. On the contrary, if RO=ESR, these transients should be spaced by a time interval long enough to allow the output voltage VOUT to stabilize itself. To have an output voltage with a step variation, the current in the inductor L must have an exponential profile with maximum slope ΔIOUT,MAX/TC at the transient instant. It is possible to have this kind of response only if the following equation, similar to eq. 4, is verified                                                         Δ              ⁢                                                           ⁢                              I                                  OUT                  ,                  MAX                                                                    ESR              ·                              C                OUT                                              ≤          m                =                              min            ⁡                          (                                                m                  p                                ,                                  m                  m                                            )                                .                                    (        9        )            
A procedure for determining the capacitance of the output capacitor based on the above considerations is described in: Redl et al., “Optimizing the load transient of the buck converter” IEEE PESC 1998; Redl et al., “Cost-optimized design of the Pentium II converter for load transient specification” PCIM 1998-Tokio; Redl et al., Analog Devices, U.S. Pat. No. 6,064,187 May 16, 2000; and Redl et al., Analog Devices, U.S. Pat. No. 6,221,302 May 8, 2001. There are also several examples about how it may be possible to realize the regulator such that ZOUT=ESR. In U.S. Pat. No. 6,064,187, a similar procedure is illustrated for the case in which, depending on the kind of the capacitor, the time constant TC=ESR·COUT is too small to satisfy eq. 9. In this case it is not possible to have ZOUT=ESR and ZOUT is chosen such that                               Z          OUT                =                  ESR          +                                                    R                O                            -              ESR                                      1              +                                                sR                  O                                ⁢                                  C                  OUT                                                                                        (        10        )                            wherein RO is the output resistance in steady state conditions, that must be greater than ESR, and s is the complex frequency. The consequence is that the response of the regulator to a variation ΔIOUT,MAX is a voltage step whose amplitude is ESR·ΔOUT,MAX followed by a further exponential increment as long as the value RO·ΔIOUT,MAX is finally reached.        
Therefore, to satisfy the specifications on the maximum voltage variation ΔVOUT,MAX it must be                               R          O                =                                            Δ              ⁢                                                           ⁢                              V                                  OUT                  ,                  MAX                                                                    Δ              ⁢                                                           ⁢                              I                                  OUT                  ,                  MAX                                                              .                                    (        11        )            
The current in the inductor has an exponential waveform but the maximum variation speed now is ΔIOUT,MAX/RO·COUT). It is then possible to choose the capacitor COUT such that the variation speed is equal to m, obtaining                               C          OUT                =                                            Δ              ⁢                                                           ⁢                              I                                  OUT                  ,                  MAX                                                                    m              ·                              R                O                                              =                                                    Δ                ⁢                                                                   ⁢                                  V                                      OUT                    ,                    MAX                                                                              m                ·                                  R                  O                  2                                                      .                                              (        12        )                                                                          
For greater values of the capacitor COUT, a smaller slope will be obtained, thus eq. 12 gives the minimum value which is necessary and sufficient to satisfy the specifications. It is easy to verify that, with the chosen values, it is indeed ESR<RO.
Generally, a regulator operates to nullify a comparison signal VCOMP that is determined in function of the output voltage VOUT and of the current flowing in the inductor IL through linear filtering operations. The comparison signal VCOMP is in general given by:VCOMP=(VOUT−V′REF)·B(s)+RSA(S)IL  (13)                 wherein s is the complex frequency and RS is a sensing resistance in series to the inductor L. The sensing resistance may even be substituted by other circuit means capable of providing a voltage signal proportional to the current circulating in the inductor, for instance a circuit having an auxiliary winding magnetically coupled to the inductor. In this case the following formulas are valid, provided that RS is the (constant) ratio between the voltage signal and the current circulating in the inductor L.        
For sake of simplicity, in the ensuing description reference will be made to the case in which the voltage signal is generated by a sensing resistance (RS).
The output impedance is given by:                               1                      Z            OUT                          =                                                            V                OUT                            -                              V                REF                ′                                                    I              OUT                                =                                                    C                ⁡                                  (                  s                  )                                                            R                S                                      +                          1                                                1                                      sC                    OUT                                                  +                ESR                                                                        (        14        )                            wherein       C    ⁡          (      s      )        =                    B        ⁡                  (          s          )                            A        ⁡                  (          s          )                      .          
In order to have ZOUT=ESR it must be                               C          ⁡                      (            s            )                          =                                            R              S                        ESR                    ·                                    1                              1                +                                                      sC                    OUT                                    ·                  ESR                                                      .                                              (        15        )            
On the contrary, if C(s) is given by                               C          ⁡                      (            s            )                          =                                            R              S                                      R              O                                ·                      1                          1              +                                                sC                  OUT                                ·                ESR                                                                        (        16        )                            an output impedance ZOUT given by eq. 10 is obtained.        
It is worth noting that only the ratio B(s)/A(s) is determined, thus it is possible to choose B(s) or A(s).
A very simple way for obtaining a voltage drop proportional to the output current consists in connecting in series to the inductor and in cascade to the feedback input of the logic command circuit CONTROL LOGIC of the switches, a resistance equal to ESR. It is easy to notice that in this way it is not possible to satisfy the condition ZOUT=ESR.
In U.S. Pat. No. 6,064,187 to Redl et al., many solutions are proposed, in which the coefficients A(s) and B(s) are                     {                                                                                                  A                    ⁡                                          (                      s                      )                                                        =                  1                                ⁢                                                                                                                                                             B                  ⁡                                      (                    s                    )                                                  =                                                                            R                      S                                                              R                      O                                                        ·                                      1                                          1                      +                                                                        sC                          OUT                                                ⁢                        ESR                                                                                                                                                    (        17        )                            and in which the resistance RO is given by eq. 11 or by eq. 7. The comparator is input with a filtered and attenuated error signal and with the voltage read on the sensing resistor. Several examples are depicted in FIGS. 4 and 5. For example, the circuit of FIG. 5 satisfies eq. 17, with RO given by eq. 7 or by eq. 11, if                     {                                                                                                                        C                      1                                        ⁢                                          1                                                                        1                                                      R                            1                                                                          +                                                  1                                                      R                            2                                                                                                                                =                                      ESR                    ·                                          C                      OUT                                                                                                                                                                                                              R                        1                                                                                              R                          1                                                +                                                  R                          2                                                                                      =                                                                  R                        S                                                                    R                        O                                                                              ⁢                                                                                                                       .                                    (        18        )                    
If RO=ESR, eq. 18 imposes that ESR be greater than RS. In other words, an equivalent output resistance RO equal to ESR is obtained using a sensing resistance RS smaller than ESR. To reduce power dissipation, it is better to choose a small sensing resistance RS, considering that RS cannot be too small otherwise the voltage drop on it would be very low.
It is worth noting that hysteretic controls are stable and operate correctly when the ripple of the comparison signal VCOMP has a substantially triangular shape. From the above equations, this ripple VCOMP,R is given by                               V                      COMP            ,            R                          =                              I            RIPPLE                    ·                      A            ⁡                          (              s              )                                ·                      R            S                    ·                                    1              +                                                sR                  O                                ⁢                                  C                  OUT                                                                                    sR                O                            ⁢                              C                OUT                                                                        (        19        )            wherein IRIPPLE is the ripple of the current in the inductor, that generally varies according to a triangular waveform. If A(s)=1, to have a substantially triangular signal VCOMP, it is necessary thatROCOUT>>TS  (20) where TS is the switching period of switches.
A problem that burdens known regulators, independently from the position in respect to the supply voltage source of the switches that drive the inductor, consists in that the comparator has an offset voltage that reduces the accuracy with which the output voltage is regulated. The offset voltage considered, VOFFSET,CMP, comprises the statistical offset, the delay effect of the comparator and an induced parasitic voltage due to the magnetic flux generated by the inductor through the circuit that generates the comparison signal VCOMP. The error on the output voltage caused by this offset voltage VOFFSET,CMP is                                           R            O                                R            S                          ·                              V                          OFFSET              ,              CMP                                .                                    (        21        )            
To reduce the parasitic voltage, which is always present, the area of this circuit is reduced as much as possible and/or this circuit is moved away from the inductor. Both expedients complicate remarkably the realization of the regulator. Another type of inaccuracy of the known regulators is caused by the oscillations of signal VCOMP due to the oscillations of the current flowing in the inductor. Referring to a constant turn on time TON regulator, the power switch (or switches) is switched to nullify the lower peak of the voltage VCOMP. Therefore, the mean value of VCOMP is half the peak-to-peak amplitude of the ripple.
In prior art regulators implementing the voltage positioning according to eqs. 13 and 17, this implies an error on the mean value of the output voltage equal to ½·RO·IRIPPLE, in respect to the desired value V′REF−RO·IO, equivalent to an error on the mean value of the current equal to ½·IRIPPLE. Similar considerations may be done for synchronous and TOFF constant controllers.